Digital information is transmitted by one or more signals using a multiplicity of methods. To generate a signal with digital information, so called digital modulation methods are used. In these methods the binary information is impressed or modulated onto a carrier. It is a characteristic of the digital modulation methods that only discrete amplitude, phase or frequency values are used for the impression, such a discrete value corresponding to a binary value or a binary sequence. In principle, these digital modulation methods are divided into amplitude shift keying, ASK for short, phase shift keying, PSK for short, or frequency shift keying, FSK for short. Combinations of amplitude, phase and/or frequency shift keying are also possible, however. Frequently, a combination of amplitude and phase shift keying is used which is also called quadrature amplitude modulation, QAM for short. Depending on the number of discrete values, it is called 16-QAM, 64-QAM etc., a discrete value in each case corresponding to a particular amplitude and phase value of the signal.
When two discrete amplitude, phase or frequency values are used, one value, as a rule, corresponds to a logical zero and the other value to a logical one. If several discrete values are used, each value corresponds to a binary sequence. In the case of four discrete values, for example, as in the case of quaternary phase shift keying, 4-PSK or QPSK for short, in which four phase states such as 0 degrees; 90 degrees; 180 degrees; 270 degrees are defined, in each case two bits per value can be transmitted (00, 01, 11, 10). In the case of eight defined values as in the case of an octonary amplitude (8-ASK), phase (8-PSK), or frequency (8-FSK) shift keying or octonary quadrature amplitude modulation (8-QAM), three bits can be transmitted simultaneously.
The use of a multiplicity of discrete values or levels is also called multi-level modulation or multi-level modulation method, respectively.
To generate multi-level signals, particularly multi-level phase-modulated or amplitude-phase-modulated signals, the so-called quadrature modulation is frequently used. In this arrangement, a generated carrier is duplicated into a first and second carrier. The first carrier is directly modulated with a first, so-called in-phase signal. The second carrier is modulated with a second, so-called quadrature signal and displaced by 90° or Pi/2 in phase with respect to the first carrier. Following this, both carriers modulated in this manner are combined again and form a so-called quadrature-modulated signal. The in-phase and quadrature signals are generated by an encoder. The latter generates the corresponding in-phase and quadrature signals from the data signal supplied. This is shown in principle in FIG. 1 for an optical transmission. A data signal, for example a 40-Gbit signal, is supplied to an encoder EN which in each case generates an in-phase and quadrature signal. These are in each case supplied to a Mach-Zehnder modulator MZM which in each case modulates a carrier which is generated by a laser diode and supplied to both Mach-Zehnder modulators MZM. One of the two modulated carriers is phase shifted by 90° or Pi/2 and the two signals are then combined by a combiner C to form a quadrature-modulated signal. This signal is transmitted by means of a transmission link US which is constructed as optical waveguide SSMF and can have dispersion-compensating means DCF and amplifiers EDFA. At the receiver end, the transmitted signal is band-pass filtered, if necessary, in a receiver RX and the two in-phase and quadrature signals are recovered with means known to the expert.
There is a number of methods available for evaluating the received in-phase and quadrature values.
The received in-phase and quadrature values are evaluated with equalizers, deciders and filters, respectively.
An equalizer in the sense of the present invention is understood to be a decider which delivers a decision in accordance with a predetermined decision space depending on the level of the signal supplied. This decision space is defined by so-called metrics.
An optimal equalization of multi-level modulation methods is known from the field of electrical communication, an implementation for arbitrary data rates being restricted by the processing speed of electronic components. An optimum equalization which may be achievable in the electrical domain is not possible, in particular, in the optical transmission with correspondingly high data rates.
An equalization is specified in US 2003/0007552 A1 which uses for this purpose a reduced alphabet equalizer with iterative equalization.
In US 2003/0063681 A1, an arrangement and a method for recognizing digital data by means of MLSE and dynamically varied trellis is specified.
In European patent application EP 1 494 413 A1, an MLSE for optical systems is specified which works with a one-dimensional metric and determines the latter.
The two in-phase and quadrature signals form the quadrature-modulated signal. This can be represented illustratively in a two-dimensional plane, the in-phase signal being shown on the X-axis and the quadrature signal being shown on the Y axis. A signal value or signal state of the quadrature-modulated signal is a point in this two-dimensional plane. The amplitude corresponds to the distance from the center point and the phase corresponds to the angle referred to the positive X axis in the counterclockwise direction. In the case of a phase modulation or phase shift keying with constant amplitude, the discrete phase values are thus located on a circle around the center point of the coordinate system and the phase angle or phase value corresponds to the angle to the positive X axis. In FIG. 2, this is shown by way of example for quaternary phase shift keying (QPSK). Four discrete phase values (45°, 135°, 225°, 315°) are shown to which a dual bit is in each case allocated (00, 10, 11, 01).
In the case of an amplitude phase modulation or quadrature amplitude modulation, respectively, discrete points are established in accordance with a raster in the two-dimensional coordinate system for a bit sequence. The angle and the distance from the center point form phase and amplitude values, respectively.